3.2 Evolution on Adaptive Landscapes Stevan J. Arnold Department of Integrative Biology Oregon State University

Thesis Models for adaptive radiation can be constructed with quantitative genetic parameters. The use of quantitative genetic parameters allows us to cross-check with the empirical literature on inheritance, selection, and population size. Stabilizing selection and peak movement appear to be necessary but may not be sufficient to account for evolution in deep time.

Outline 1.Evolution without selection, genetic drift. 2.Univariate evolution about a stationary peak. 3.Bivariate evolution about a stationary peak. 4.Evolution when the peak moves. 5.Challenging the models with data

1. Evolution without selection, genetic drift a.Sampling N e individuals from a normal distribution of breeding values b.Projecting the distribution of breeding values into the future Generation Lineage mean

1. Evolution without selection, genetic drift c. Many replicate populations evolving by drift Generation Lineage mean Animation 1

2. Univariate evolution about a stationary peak a. Tendency to evolve uphill on the adaptive landscape b. Stochastic dynamics with a single Gaussian, stationary peak The Ornstein-Uhlenbeck, OU, process Per generation change in mean Variance among replicate lineages in trait mean

2. Univariate evolution about a stationary peak b. Stochastic dynamics with a single, stationary peak Generation Lineage mean

3. Bivariate evolution about a stationary peak a. Deterministic response to a single Gaussian, stationary peak The spaceship model Lineage mean for trait 1 Lineage mean for trait 2 Animation 2

3. Bivariate evolution about a stationary peak b. Stochastic response to a single Gaussian, stationary peak Drift-selection balance, the OU process Lineage mean for trait 1 Lineage mean for trait 2 Animation 3

3. Bivariate evolution about a stationary peak b. Replicate responses to a single Gaussian, stationary peak The adaptive landscape trumps the G-matrix Lineage mean for trait 1 Lineage mean for trait 2

3. Bivariate evolution about a stationary peak b. Stochastic response to a single Gaussian, stationary peak The adaptive landscape trumps the G-matrix Lineage mean for trait 1 Lineage mean for trait 2 The heartbreak of OU: to account for data, requires small N e or very weak stabilizing selection (large ω)

4. Evolution when the peak moves a. Brownian motion of a Gaussian adaptive peak The optimum, θ, undergoes Brownian motion The lineage mean chases the optimum

4. Evolution when the peak moves a. Brownian motion of a Gaussian adaptive peak Replicate lineages respond to replicate peak movement

4. Evolution when the peak moves b. White noise motion of a Gaussian adaptive peak The optimum, θ, undergoes white noise movement The lineage mean chases the optimum

4. Evolution when the peak moves b. White noise motion of a Gaussian adaptive peak Replicate optima, θ, undergo white noise movement Replicate lineage means chase the optima

4. Evolution when the peak moves c. Multiple burst model of peak movement The optimum, θ, moves in rare bursts, governed by a Poisson process, but is otherwise stationary The lineage mean instantaneously tracks bursts in the optimum, but otherwise evolves according to a white noise process Generation Lineage mean θ θ

5. Challenging the models with data The data Longitudinal data: 6,053 values for change in trait mean over intervals ranging from one to ten million generations; 169 sources, time series. Tree-based data: 2,627 node-average divergence estimates; 37 time-calibrated phylogenies. Traits: size and counts; dimensions and shapes of shells, teeth, etc.; standardized to a common scale of within-population, phenotypic standard deviation. Taxa: foraminiferans … ceratopsid dinosaurs. …

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5. Challenging the models with data a. Brownian motion, the genetic drift version Too little differentiation on short timescales, too much on long timescales B Animation 4

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Model White noise parameter estimate ( σ ) AIC* White noise (WN) only0.20− Brownian motion + WN0.11− Single-burst + WN0.10− Multiple-burst + WN0.10− Challenging the models with data

Burst timing distribution (mean time between bursts = 25 my) White noise distribution (dashed) Burst size distribution (solid) Probability Divergence B C A Interval (years) 5. Challenging the models with data

What have we learned? 1.Quantitative genetic models can be used to model adaptive radiations. 2.Models in which an adaptive peak is stationary can not account for the scope of actual adaptive radiations. 3.Bounded evolution is a prevalent mode of evolution on all timescales. 4.Sudden departures from bounded evolution are rare but may account for the invasion of new adaptive zones.

References Lande, R Natural selection and random genetic drift in phenotypic evolution. Evolution 30: Lande, R Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry. Evolution 33: Lande, R Sexual dimorphism, sexual selection, and adaptation in polygenic characters. Evolution 34: Hansen, T. F., and E. P. Martins Translating between microevolutionary process and macroevolutionary patterns: the correlation structure of interspecific data. Evolution 50: Hansen, T. F., J. Pienaar, and S. H. Orzack A comparative method for studying adaptation to a randomly evolving environment. Evolution 62: Estes, E. & S. J. Arnold Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales. American Naturalist 169: Uyeda, J. C., T. F. Hansen, S. J. Arnold, and J. Pienaar The million-year wait for macroevolutionary bursts. Proceedings of the National Academy of Sciences U.S.A. 108: Arnold, S. J Phenotypic evolution, the ongoing synthesis. American Naturalist 183: